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100

 Evaluate the limits using basic limit 

  • Limx→2(x)

  • Limx→2(5)

Limx→2(x) = 2

Limx→2(5) = 5

100

Name the three types of discontinuities

removable, jump, infinite

100

limx→-1g(x)=??

limx→-1g(x)=3

100

Write the point-slope form equation of the line that passes through:

(-10, 3) and (23, 4).

y = (1/33)x + 109/33

100

What is the definition of an inverse function? (formula)

f-1(f(x)) = x


200

Evaluate Limx→-2(3x3-2x+7)

Limx→-2(3x3-2x+7) = 3(-2)3 - 2(-2) + 7 = 13

200

What are the three conditions that continuity requires

f(a) exists, Limx→af(x) exists, Limx→af(x)=f(a)

200

Slide 3

Limx➝2-f(x) = 8

Limx➝2+f(x) = 3

Limx➝2f(x) = DNE

200

Write the following equation in equivalent exponential form.

                            log (100) = 2

102 = 100

200

How can you determine if a function is even or odd?

f(-x) = f(x) means even; f(-x) = -f(x) means odd

300

Write out the limit laws to: sum, difference, constant multiple, product, quotient, power, and root in regards to Limx→a of f(x) and g(x)

slide 2

300

determine whether f(x)=x+2x+1 is continuous at x= -1, classify the continuity

 f(x)=x+2x+1 →  f(-1)=-1 +2-1 +1 = 10, undefined, therefore discontinuous

Limx→-1-  f(x)= - infinity and Limx→-1+  f(x)= + infinity, infinite discont. 

300

Find the following (slide 7)

  • Limx→ -2- f(x); Limx→ -2+ f(x); Limx→ -2 f(x)

  • Limx→ 2- f(x); Limx→ 2+ f(x); Limx→ 2 f(x)

Slide 8

300

 Which of the following is not a trig identity?

a) 1 + tan^2(x) = sec^2(x)

b) 1 + cot^2(x) = csc^2(x)

c) tan^2(x) - 1 = sec^2(x)

d) tan(x) = sin(x)/cos(x)

C

300

Slide 14

Slide 15

400

Use limit laws to evaluate Limx→6(2x-1)(x+4)), indicating the limit law

1) product: Limx→6(2x-1) x Limx→6(x+4))

2) difference and root: (Limx→6(2x) - Limx→6(1)) x (Limx→6(x+4))

3) constant and sum: (2Limx→6(x) - Limx→6(1)) x (Limx→6(x) + Limx→6 (4))

Evaluate: (2(6)-1) x  ((6) + 4)

 Limx→6(2x-1)(x+4)) = 1110

400

Take the intervals over which the function:

f(x)=x-1x2+2xis continuous

A= x2+2x; x= -2 and 0, discontinuous at those points b/c you can’t have #/0, thus continuous intervals are (-∞, -2) U (-2,0) U (0, ∞)

400

Slide 9

(slide 10)

  • Limx→ -2 [2f(x) + g(x)]

  • Limx→ -2 [2f(-2) + g(-2)] = (2)(3) + (0) = 6

  • Limx→ -2 [f(x) x g(x)]

  • Limx→ -2 [f(-2) x g(-2)] = (3)(0) = 0

  • Limx→ -2 [g(f(x))]

  • Limx→ -2 [g(f(-2))] = Limx→ -2 g(3) = 2

  • Limx→ 0

  • g(x)= DNE


400

Find the amplitude, period and phase shift with direction for the following function: y=-3+4sin(2x+π)

Amplitude: 4; period: π; phase shift: left π, down 3

400

Slide 16

Slide 12

500

Apply squeeze theorem to evaluate Limx→0(xcosx)

Limx→0(xcosx)=0 (full workup is in slide 1)

500

Sketch a graph of the function y = f(x) with the following:

  • Domain of f is [0,5]

  • Limx→1+f(x) and the Limx→1-f(x) exists and are equal

  • f(x) is left continuous but not continuous at x=2, and right continuous but not continuous as x=3

  • f(x) has a removable discontinuity at x=1, a jump discontinuity at x=2, and the following limits hold:

    • Limx→3-f(x)= -∞

    • Limx→3+f(x)= 2

Slide 6

500

Sketch a graph with the following properties

  • Limx→2f(x)=1, Limx→4-f(x)=3), Limx→4+f(x)=6, f(4) is not defined

Slide 5

500

Verify that the following equation is an identity.

sinx/(sinx + cosx)= (tanx)/(1 + tan x)

Slide 13

500

If f(x) is continuous over [0,2], f(0)>0 and f(2)>0, can we use IVT to conclude that f(x) has no zeros in the interval [0,2]? Explain.

Slide 11